Conversion = Desire - Friction, more or less

One of my favorite equations for a while has been the very simple Conversion = Desire - Friction,  I have always said that I did not think the math was right but it was so simple and deliciously directionally perfect.  Serious credit to Sean Ellis on it (I believe this is his baby).  More desire, less friction, all good. Made me happy too : )  One day I was thinking that the right answer is actually conversion = p(desire>friction). So if you have a distribution of desire and a distribution of friction for a population, the actual conversion will be those where, for an individual, desire is greater than friction.

All kind of questions start swirling.  Are we better off making desire just a tiny bit better than friction everywhere?  Stop effort once we have motivated conversion, anything beyond that is wasted.  Are there business models where desire distributions or friction distributions should be dictating approaches that we are not thinking about that well yet?  Probably.  Gimme some time to grok on that or some help at least.

Simple enough I guess. But it is rare that the conversion event is enough. Loyalty, LTV, advocacy all go way past conversion.  So even if we get the conversion event perfectly modeled it may not help us succeed better. If upfront conversion and promoter score were independent, maybe, but we all know they are not. 
 
So if you have the data to think about audience desire and friction distribution, and can build these things independently and impact downstream behavior. You should use a more refined equation perhaps. But for most of us, we are better off keeping it simple probably.  Geez, it is hard enough getting statistical significance on a test as we fragment markets more and more anyway.  I will probably stay with the directional goal of increase desire and reduce friction broadly most of the time for now.  But I am keeping my eye out for a place to apply a more refined view to good effect.  I am sure it is out there for some high scale consumer model.  Seen it?